The correlation of fractal structures in the photospheric and the coronal magnetic field

TL;DR

This study investigates the relationship between fractal properties of photospheric magnetic patterns and coronal magnetic fields, finding no correlation under nonlinear force-free extrapolation but some correlation at the potential field level, highlighting the complexity of magnetic field transitions.

Contribution

It demonstrates that the transition from photospheric to coronal magnetic fields complicates the correlation of their fractal properties, especially under nonlinear force-free conditions.

Findings

No correlation between photospheric and coronal fractal dimensions with nonlinear force-free extrapolation.

Significant correlation observed only at the potential field (current-free) level.

Transition from non-force-free to force-free fields hampers direct fractal correlation.

Abstract

This work examines the relation between the fractal properties of the photospheric magnetic patterns and those of the coronal magnetic fields in solar active regions.Our results show no correlation between the fractal dimensions of the observed 2d photospheric structures and the extrapolated unstable volumes in the corona, when nonlinear force-free extrapolation is used. This result is independent of efforts to (1) bring the photospheric magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the lower part of the modeled magnetic field volume that is almost completely filled by unstable volumes. A significant correlation between the fractal dimensions of the photospheric and coronal magnetic features is only observed at the zero level (lower limit) of approximation of a current-free (potential) magnetic field extrapolation. We conclude that the complicated transition from photospheric non-force-free fields to coronal force-free ones hampers any direct correlation between the fractal dimensions of the 2d photospheric patterns and their 3d counterparts in the corona at the nonlinear force-free limit.